Probabilistic models for particle and scalar transport in fluctuating flows: an evaluation of simple closure approximations

Kinetic modeling of particles in stratified flow – Evaluation of dispersion tensors in inhomogeneous turbulence

“…The passive scalar approximation (PSA) for c i The analysis of Swailes and Darbyshire (1999) and Reeks (1992), shows indirectly that in the passive scalar limit (s p ! 0), one can relate c i directly to k ij , when we impose that the density should be constant in the limit (''well mixed condition'').…”

“…For further comparison to Swailes and Darbyshire (1999) and Reeks (1992), it is convenient to rewrite the 1D momentum equation as a diffusion equation expressing the different mass flux contributions. In the 1D stationary case and for all s p , the perpendicular mass flux is generally…”

“…For example, deposition rates near boundary layers and particle transport within the bulk of the carrier fluid may depend strongly on turbulence inhomogeneity, and one would therefore prefer a model which can handle the associated effects on the particle concentration and the particle kinetic stress. Kinetic theories for dilute suspensions (e.g., Reeks, 1992Reeks, , 2005Swailes and Darbyshire, 1999;Hyland et al, 1999;Sergeev et al, 2002;Zaichik and Alipchenkov, 2005) are sufficiently general such that turbulence inhomogeneity is accounted for in a consistent manner. A common factor in these theories is that they are formulated in terms of a conservation equation for the particle probability distribution function (PDF).…”

A statistical model for predicting the fluid displaced/added mass and displaced heat capacity effects on transport and heat transfer of arbitrary-density particles in turbulent flows

“…Statistical models of transport and dispersion in two-phase dispersed turbulent flows were developed by a number of authors (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]). However, all these works fall in turbulent flows laden with heavy particles, whose density is much more than that of the carrier fluid and when the drag force of all the interfacial forces is only essential.…”

“…In the framework of the approach being considered, Eqs. (A6) and (A7) are solved using the iteration method, whereas Hyland et al [8], Smailes and Darbyshire [10], and Skartlien et al [20] tackled the problem by solving an equation for Green's function. It can be shown that both approaches are equivalent in a near-homogeneous Gaussian fluid flow field at long time in reference to the fluid integral timescale when initial conditions may be neglected.…”